Dear PARI developers,
I have fixed a problem with ellorder found by John Cremona:
It was not possible to ask for the order of a point over a Fp when the curse was
defined over Z. i.e
? ellisoncurve(ellinit([0,0,0,0,2],1),[-1,-1]*Mod(1,101))
%2 = 1
? ellorder(ellinit([0,0,0,0,2],1),[-1,-1]*Mod(1,101))
%1 = 0
did not work.
Also I did some archeology and actually ellorder already existed in version 2.0.17
and the code was:
GEN
orderell(GEN e, GEN p)
{
...
p1=p; k=1;
for (k=1; k<16; k++)
{
if (lg(p1)<3) { avma=av; return stoi(k); }
p1 = addell(e,p1,p);
}
avma=av; return gzero;
}
so the ellorder slowness for large non-torsion point is not a new feature.
Cheers,
Bill.